{"ID":3053223,"CreatedAt":"2026-06-04T04:41:36.695875263Z","UpdatedAt":"2026-06-05T19:35:40.366641076Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04176","arxiv_id":"2606.04176","title":"Low-rank Distributional Matrix Completion","abstract":"We study a distributional generalization of the matrix completion problem in which each entry of the target matrix is a probability distribution rather than a scalar. In this setting, only a subset of matrix entries is observed, and even for observed entries, the underlying distributions are not directly accessible; instead, we observe finitely many samples drawn from them. To represent distributional entries, we employ kernel mean embeddings and introduce a notion of Tucker rank for distribution-valued matrices to capture their low-rank structure. The infinite-dimensional nature of kernel embeddings poses significant methodological challenges. To address this, we introduce functional unfolding operators that link the proposed distributional low-rank structure to the classical Tucker rank for finite-dimensional tensors. Based on this framework, we propose a novel estimator for distributional matrix completion. We establish non-asymptotic error bounds that characterize the statistical performance of the estimator. Extensive experiments on synthetic data and a real-world application demonstrate the effectiveness of the proposed method.","short_abstract":"We study a distributional generalization of the matrix completion problem in which each entry of the target matrix is a probability distribution rather than a scalar. In this setting, only a subset of matrix entries is observed, and even for observed entries, the underlying distributions are not directly accessible; in...","url_abs":"https://arxiv.org/abs/2606.04176","url_pdf":"https://arxiv.org/pdf/2606.04176v1","authors":"[\"Jiayi Wang\",\"Raymond K. W. Wong\"]","published":"2026-06-02T19:41:07Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.ST\",\"stat.ML\"]","methods":"[]","has_code":false}